R. Menezes

New global defect structures

We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and finding explicit solutions.

Braneworld models of scalar fields with generalized dynamics

This work deals with braneworld models driven by real scalar fields with nonstandard dynamics. We develop the first-order formalism for models with standard gravity but with the scalar fields having generalized dynamics. We illustrate the results with examples of current interest, and we find analytical and numerical solutions for warp factors and scalar fields. The results indicate that the generalized braneworld scenario is classically stable, and capable of localizing gravity.

First-order formalism and dark energy

This work deals with cosmological models driven by real scalar field, described by standard dynamics in generic spherical, flat, and hyperbolic geometries. We introduce a first-order formalism, which shows how to relate the potential that specifies the scalar field model to Hubbles parameter in a simple and direct manner. Extensions to tachyonic dynamics, and to two or more real scalar fields are also presented.

Generalized global defect solutions

We investigate the presence of defect structures in generalized models described by a real scalar field in (1,1) space-time dimensions. We work with two distinct generalizations: one in the form of a product of functions of the field and its derivative, and the other as a sum. We search for static solutions and study the corresponding linear stability on general grounds. We illustrate the results with several examples, where we find stable defect structures of modified profile. In particular, we show how the new defect solutions may give rise to evolutions not present in the standard scenario in higher spatial dimensions.

f(R)-Brane

We investigate the existence of brane solutions in braneworld scenarios described by real scalar field in the presence of modified f(R) gravity with a single extra dimension. In the case of constant curvature, we obtain first-order differential equations which solve the equations of motion and ease the search for explicit analytical solutions. Several examples of current interest are investigated to illustrate the results of the present work.

First-order framework and generalized global defect solutions

This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we search for first-order differential equations which solve the equations of motion. The main issue concerns the introduction of a new function, which works like the superpotential usually considered in the standard situation. We investigate the problem in the general case, with an arbitrary number of fields, and we present several explicit examples in the case of a single real scalar field.

Generalized self-dual Chern-Simons vortices

We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex solution found in the standard Chern-Simons model.

BPS Solutions to a Generalized Maxwell-Higgs Model

We look for topological BPS solutions of an Abelian Maxwell–Higgs theory endowed by non-standard kinetic terms to both gauge and scalar fields. Here, the non-usual dynamics are controlled by two positive functions, G(|ϕ|) and w(|ϕ|), which are related to the self-dual scalar potential V(|ϕ|) of the model by a fundamental constraint. The numerical results we found present interesting new features, and contribute to the development of the recent issue concerning the study of generalized models and their applications.

Classical behavior of deformed sine-Gordon models

Abstract In this work we deform the ϕ 4 model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions that they engender. In particular, we introduce non-polynomial potentials which support some exotic two-kink solutions.

Perturbative aspects and conformal solutions of F(R) gravity

Abstract We investigate perturbative aspects of gravity with a general F ( R ) Lagrangian, as well as nonperturbative dilatonic solutions. For the first part, we are interested in stability and the definition of asymptotic charges. The main result of this study is that, while generic F ( R ) theories are stable under metric perturbations, they are expected to show instabilities against curvature perturbations when the Lagrangian includes 1 / R terms. For the second part, one is interested on exact solutions, and we explicitly construct kink-like solutions of the Liouville type for the dilaton field for F ( R ) having the form R + γ R n , in two and in four dimensions.